First of all, excuse my bad English - I'm German, but I do my
best to express myself understandably. I try to bring WinUAE on my Smart TV (49'') as a screen, with the aim
of playing my childhood games in large format (3480x2160). The
problem with that is that although I managed to project the games
on the whole screen, they are now very slow. The sound hooks, the
charging process takes a long time, everything seems very
time-delayed. Is that a known quirk because I'm just using too
much resolution for the old games, or am I able to experiment
with the settings a bit? I would be very grateful for your help.

Hardware specs, please. Does both PC and TV support 50Hz/60Hz at 4k resolutions? Max 30Hz (or ~24Hz) would not work very well and would most likely cause bad side-effects.

I don't recommend resolutions that are not 100% native panel integer divisible, like 640x480 because TVs generally don't scale PC-only resolutions very well and when letting GPU do the scaling, you at least have some control of the result. (via UAE filter or GPU control panel)